Primitive Element Theorem

Theorem

Let $E / F$ be a separable field extension of finite degree.

Then $E / F$ is simple: there exists $\alpha\in E$ such that $E = \map F \alpha$.

Proof

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Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): simple extension